Republicans now have control of the House and have chipped away at the Democrats’ majority in the Senate. What they likely won’t have control over is the badly broken housing market, persistently high unemployment and runaway government spending.

Politicians’ promises aside, solving those issues will take much more than just a change on the nameplates at congressional offices. And the gridlock in Washington is likely to make solving the nation’s economic problems even more difficult.

“The Democrats had a very hard time getting legislation passed, even with the solid majority that they had,” said Sam Stovall, chief investment strategist at Standard & Poor's. “I don't think the Republicans are going to do any better with only a very slim majority in the House and no majority at all in the Senate.”

House Republican leader John Boehner vowed Wednesday to work to roll back the Obama administration's health care reform. The Ohio Republican is in line to replace California Democrat Nancy Pelosi as House Speaker.

"I think it's important for us to lay the groundwork before we begin to repeal this monstrosity and replace with it commonsense reforms that will bring down the cost of health care in America," Boehner told reporters.

Some House Republicans have also vowed to seek changes in the sweeping package of financial regulatory reforms know as Dodd-Frank. Rep. Spencer Bachus, R, Ala., who is set to replace Masschusetts Democrat Barney Frank as chairman of the House Financial Service Committee, said the effort would involve targeting "job-killing provisions" of the law.

"We will take incremental steps knowing we have to have bipartisan agreement in the Senate," he told CNBC.

As control of the House shifts to a new set of GOP leaders, Congress faces a familiar set of economic issues: housing, jobs and the budget deficit.

HousingNow entering its fourth year of falling prices and rising foreclosures, the ailing housing market continues to weigh on economic growth. Three separate federal programs have tried, and failed, to turn the tide on foreclosures. Tuesday’s election isn’t likely to change that.

“There is no magic bullet solution at the federal level to fix the housing market,” said Jared Seiberg, a financial services policy analyst at MF Global's Washington Research Group. “That’s true whether Republicans have veto-proof majorities in the House or Senate or Democrats do. If the Obama administration could have done that in the past two years, it would have.”

Neither party has figured out how to slow the pace of foreclosures, keep more families in their homes or offer relief to the one in four mortgage holders who are "under water," owing more than their homes are worth. Splitting control of Congress won’t make it any easier to fix the money-losing government-controlled mortgage giants Fannie Mae and Freddie Mac. If anything, the debate could become more polarized.

“You’re going to have subcommittee chairmen on the House side who question whether the government should be playing the role that it has historically played for the past several generations in the mortgage market," said Seiberg.

Recent disclosures that lenders might have cut corners in their efforts to foreclose on homeowners have prompted an investigation by all 50 state attorneys general. That effort is being lead by Iowa's Tom Miller, who won a tough re-election fight Tuesday.

Taxes and spendingVoters who demanded change in Washington will see significant change in the House leadership, as control of key committees shifts to the GOP. Republicans have promised major changes in policies related to taxes and spending.

One key leadership change will put Rep. Paul Ryan, R-Wis., in charge of the House Budget Committee, which proposes spending targets and estimates tax revenues. A vocal opponent of record federal budget deficits, Ryan has proposed "A Roadmap for America's Future" that would bring deep cuts in spending.

Republicans also would control the House Appropriations Committee, where they have vowed to save $100 billion next year by cutting spending to 2008 levels, with exceptions for programs for the elderly, U.S. troops and military veterans. Ranking California Republican Jerry Lewis, who chaired the panel during the George W. Bush administration, would need a term limits waiver from GOP leaders to get back the job. Next in line would be Rep. Harold Rogers, R.-Ky., who has been lobbying party colleagues for the job.

JobsThose spending cuts would likely bring steeper cuts in government payrolls, which have shrinking as the impact of the federal stimulus program has begun to fade. Since peaking in April, 2009, a net 450,000 government jobs have been eliminated. Those payrolls are expected to continue shrinking as states struggle to close multibillion-dollar budget gaps.

Some business leaders have expressed reluctance to hire more workers until the economic outlook improves – and they get more clarity about tax policies and the cost of health care reform. Dave Camp, R-Mich., is in line to chair the tax-law-writing House Ways and Means Committee. Camp is among Republicans who have pledged to cut taxes in an effort to spur job creation.

Though some economists have argued that another round of stimulus spending is needed to create jobs, that idea already faces strong resistance from both parties. Rep. Darrell Issa, R-Calif., who is in line to take control of the House Oversight and Government Reform Comimttee, has promised to review the effectiveness of the Obama administration's $814 billion stimulus program.

One Tuesday, Issa told reporters he will work to grant subpoena power to government inspectors general, and begin investigations into Fannie Mae and Freddie Mac.

Some have argued that by restraining Congress, gridlock can be a good thing. But that argument is easier to make when the economy is on track, said investment adviser Ron Carson.

“Today things are broken,” he said. “What we need today is decisive leadership and action. And you're not going get that with gridlock.